The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1 2X 4X  1  X  1  1  1  1  1  1  1  1  1  0  1  1  1  1  X  1  1  1  1  1  1 3X  1 3X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 3X  1  1  1  1  1  1
 0  1  0 3X 2X  X  1 3X+2 3X+3 3X+1 2X+1 4X+1 3X+4 2X+4  2  1  1 2X+3  1 X+1 4X+2 4X+4  3 X+2  3 X+4 2X 4X  1  4 3X+2 X+3 2X+3  1 2X+4 4X+3  1 4X+1 3X+3 3X+1  1 2X+2  1 X+2 3X+2 X+2 4X+3 4X+3 X+1  0  4 4X X+4 4X 2X+3  2 X+3 3X+1 X+1  4 2X+3  1 X+4  3 3X+4  2  X 2X+1
 0  0  1 3X+1  2  4 X+4 3X+4 4X+4 3X+2 3X+3  X X+2 3X 2X+2 3X+2  1  0 4X+3 4X+1 2X+1 2X+3  3 4X 2X+1 4X+1 3X+1 X+3 2X+4 X+4  2 X+2 4X+4 4X+1 4X+2 2X+1 2X+2  1 4X 3X+3 2X+2 2X+4 X+4  1  3 3X 3X+1 4X+3 X+3 3X+3 2X+4 2X X+1 3X+2  3  X 3X+4 2X+3  0 4X+1 3X+1 4X+3 X+3 4X+3 3X+3 4X+2 2X+1 2X+4

generates a code of length 68 over Z5[X]/(X^2) who´s minimum homogenous weight is 262.

Homogenous weight enumerator: w(x)=1x^0+1400x^262+380x^263+720x^264+500x^265+2600x^267+1000x^268+320x^269+480x^270+1900x^272+800x^273+300x^274+312x^275+1380x^277+480x^278+360x^279+116x^280+1140x^282+340x^283+300x^284+204x^285+580x^287+12x^290

The gray image is a linear code over GF(5) with n=340, k=6 and d=262.
This code was found by Heurico 1.16 in 17.6 seconds.